Standard deviation

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Pia compares quiz scores from two classes. Class A: mean 78, SD 4. Class B: mean 78, SD 12. Which statement do the summaries support?

   • Class B did better, because its standard deviation is larger.
   • The classes did equally well, so their scores look alike.
   • Class A's scores are more spread out, because its SD of 4 is smaller.
   • Both classes average 78, but Class B's scores are more spread out.
2. 2.

   Noah can leave 25 minutes before class. Route A: mean 20 minutes, SD 8. Route B: mean 22 minutes, SD 2. Which route is safer for arriving on time?

   • Route A, because its mean time of 20 minutes is shorter than Route B's mean of 22.
   • Route A, because its larger SD means steadier trips that rarely run past 25 minutes.
   • Route B: trips average 2 minutes longer but stay near 22, so it is rarely late.
   • Route A, because a larger SD means faster trips, so its trips will be shorter.
3. 3.

   Esme wants plants of nearly equal height. Fertilizer X: mean growth 12 cm, SD 1. Fertilizer Y: mean growth 12 cm, SD 5. Which should Esme use?

   • Fertilizer X: the same average growth, but heights stay closer together.
   • Fertilizer Y, because its SD of 5 means heights stay closer together.
   • Fertilizer Y, because a larger SD means taller plants.
   • Either one, because the two means are equal, so the plants will be alike.
4. 4.

   Milo wants the more consistent team. Team A: mean 14 points, SD 2. Team B: mean 17 points, SD 9. Which team is more consistent?

   • Team A is more consistent, even though Team B scores more on average.
   • Team B is more consistent, because its mean of 17 is higher.
   • Team B is more consistent, because a larger SD means better scores.
   • Team B is more consistent, because its larger SD means steadier scores.
5. 5.

   Kira's race times have an SD of 1.5 minutes. Every time is multiplied by 60 to give seconds. What is the SD in seconds?

   • 1.5 seconds
   • 61.5 seconds
   • 8,100 seconds
   • 90 seconds
6. 6.

   Every plant grows exactly 2 cm taller. Before, the mean was 30 cm and the SD was 1.8 cm. Tala asks: what is the SD after?

   • 3.6 cm
   • 32 cm
   • 3.8 cm
   • 1.8 cm

7. Read this first

   Pia

   Score 94 on a test with mean 80, SD 7. Bo: score 84 on a test with mean 70, SD 4.

8. 7.

   Zee compares scores on two different tests. Whose score stands higher compared with its own test's mean and SD?

   • They are equal, because each score is 14 points above its mean.
   • Bo: 84 is 3.5 SDs above its mean, while Pia's 94 is 2 SDs above.
   • Pia, because the SD of 7 is larger than 4, so Pia has more room above the mean.
   • Pia, because 94 is higher than 84, so Pia stands higher on a test.

9. Kira

   150 cm in a row with mean 120 cm, SD 15 cm. Zee: 70 cm in a row with mean 50 cm, SD 5 cm.

10. 8.

    Luz compares sunflowers from two different rows. Which sunflower is taller compared with its own row's mean and SD?

    • Zee: 70 cm is 4 SDs above its mean, while Kira's 150 cm is 2 SDs above.
    • Kira, because 150 cm is taller than 70 cm, so Kira's sunflower stands higher.
    • Kira, because 30 cm above the mean is more than Zee's 20 cm.
    • Kira, because the SD of 15 is larger than 5, so Kira has more room above the mean.
11. 9.

    62 in a game with mean 50, SD 8. Luz: 41 in a game with mean 30, SD 4. Ari compares scores in two different games. Whose score stands higher compared with its own game's mean and SD?

    • Jun, because the SD of 8 is larger than 4, so Jun has more room above the mean.
    • Luz: 41 is 2.75 SDs above its mean, while Jun's 62 is 1.5 SDs above.
    • Jun, because 62 is higher than 41, so Jun's score stands higher in the game.
    • Jun, because 12 points above the mean is more than Luz's 11.

12. Tala

    3.2 m on a team with mean 2.6 m, SD 0.2 m. Noah: 2.1 m on a team with mean 1.8 m, SD 0.1 m.

13. 10.

    Bo compares long jumps on two different teams. Whose jump stands higher compared with its own team's mean and SD?

    • They are equal: each jump is 3 SDs above its team's mean.
    • Tala, because 0.6 m above the mean is more than Noah's 0.3 m.
    • Tala, because 3.2 m is longer than 2.1 m.
    • Tala, because the SD of 0.2 is larger than 0.1.